Topic: Common Core Learning Standards

Jan 26, 2016 - Topic C is a capstone topic for this module, where students use what they have learned about probability and expected value to analyze strategies and make decisions in a variety of contexts (S.MD.B....

Jan 26, 2016 - In this topic, students first distinguish between discrete and continuous random variables and then focus on probability distributions for discrete random variables. In the early lessons of this...

Jan 26, 2016 - In this topic, students extend their understanding of probability, building on work from Grade 11. The multiplication rule for independent events introduced in Grade 11 is generalized to a rule that...

Jan 26, 2016 - The graphs of the trigonometric functions are revisited in Topic C. Students visualize these graphs with the aid of the appropriate software and briefly recall how changing various parameters of a...

Jan 26, 2016 - Students derive sophisticated applications of the trigonometric functions in Topic B including: the area formula for a general triangle, the law of sines, the law of cosines, and Heron’s formula. ...

Feb 09, 2016 - Topic A helps students recall how to use special triangles positioned within the unit circle to determine geometrically the values of sine, cosine, and tangent at special angles. The unit circle is...

Jan 26, 2016 - In Topic C students study inverse functions, being careful to understand when inverse functions do and do not exist, working to restrict the domain of a function to produce an invertible function. ...

Jan 26, 2016 - In Topic B, students explore composition of functions in depth and notice that a composition of a polynomial function with the function f(x) = 1/x gives functions that can be written as ratios of...

Jan 26, 2016 - Topic A brings students back to the study of complex roots of polynomial functions. Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...

Jan 26, 2016 - The module concludes with Topic E focusing on the properties of quadrilaterals inscribed in circles and establishing Ptolemy's theorem. This result codifies the Pythagorean theorem, curious facts...

Jan 26, 2016 - Topic D brings in coordinate geometry to establish the equation of a circle. Students solve problems to find the equations of specific tangent lines or the coordinates of specific points of contact...

Jan 26, 2016 - In Topic C, students explore geometric relations in diagrams of two secant lines, or a secant and tangent line (possibly even two tangent lines), meeting a point inside or outside of a circle. They...

Jan 26, 2016 - Topic B defines the measure of an arc and establishes results relating chord lengths and the measures of the arcs they subtend. Students build on their knowledge of circles from Module 2 and prove...

Jan 26, 2016 - Topic A leads students first to Thales' theorem (an angle drawn from a diameter of a circle to a point on the circle is sure to be a right angle), then to possible converses of Thales' theorem, and...

Jan 26, 2016 - In Topic E students apply the knowledge developed in this module to understand how first-person video games use matrix operations to project three-dimensional objects onto two-dimensional screens and...

Jan 26, 2016 - Topic D opens with a formal definition of a vector. The arithmetical work for vector addition, subtraction, scalar multiplication, and vector magnitude is explored along with the geometrical...

Jan 26, 2016 - Topic C provides a third context for the appearance of matrices via the study of systems of linear equations. Students see that a system of linear equations can be represented as a single matrix...

Jan 26, 2016 - In Topic A, students look at incidence relationships in networks and encode information about them via high-dimensional matrices. Questions on counting routes, the results of combining networks,...

Jan 26, 2016 - Topic C highlights the effectiveness of changing notations and the power provided by certain notations such as matrices. The study of vectors and matrices is introduced through a coherent connection...

Jan 26, 2016 - In Topic B, students develop an understanding that when complex numbers are considered points in the Cartesian plane, complex number multiplication has the geometric effect of a rotation followed by...

Jan 26, 2016 - Topic A begins the study of linearity looking at common misconceptions made by math students. This study leads to complex solutions which launches the study of products, quotients of complex numbers...

Apr 06, 2016 - Throughout their math experiences, students will look for and make use of structure (MP.7). In Topic F, children model repeating and growth patterns using objects, sounds, and movements.

Jan 26, 2016 - Topic E builds on the work of previous topics, providing opportunities for children to solve subtraction story problems with abstract representations (MP.4). As in Topic D, children decontextualize...